The third is more elementary; it contains a full, yet brief definition of all the terms made use of in the theory." The fourth fection contains the whole theory, respecting planes and right lines. The firft eight theorems, refpe&t vanifhing lines only, except the first, and the corollaries, deduced from feveral, which are also usefulleffons, for practice. The 9th, 10th, and 12th theorems are most effential in practice. In the 10th and its corollaries is fhewn how to manage the representations of figures, in planes which are parallel to the picture. First that the lines in the reprefentations are parallel to the originals, and have that ratio to the originals, as the distance of the picture to the distance of the plane they are in. In figure of the annexed plate, A B is the picture, parallel to the plane ghi, in which is fituated the line N O, or R S. The vifual rays, E N, E O, being drawn, cut the picture in the points n and o, their reprefentations; and the plane NEO, cuts the picture in no, the reprefentation of NO; for the eye (at E) being in that plane, and, in the vertex of the angle NEO, confequently, the line n o, the fection of that plane with the picture is parallel to the original (NO) seeing they are in parallel planes (16. 11. Eu.) and, because they are parallel, the triangles, NEO n E o, are fimilar; and confequently, no: NO:: En: EN. i. e. as EC to Ef, the distance of the picture to the distance of the plane ghi. The fourth corollary, fays, The angle which the reprefentations any two original lines, that are parallel to the picture, make with each other, is equal to the angle made by the originals. For, the reprefentations are, refpectively, parallel to the originals. This neceffarily follows from Pr. 10th of the 11th of Euclid. Corollary 5. fums up, in brief, the real ufe of all that is inculcated by this theorem, viz. that the reprefentations of all figures, in planes parallel to the picture, are fimilar to their originals; and have a certain proportion to them. For, by the theorem, each line, fo fituated, is represented by a parallel line; which has that proportion to the original, as the diftance of the picture, to the diftance of the original plane, fuch line is in. Confequently, every fide, of figures, in planes fo fituated, have the fame ratio to its original; and, by the fourth corollary it is manifeft, that each angle, in the reprefentation, is equal to its correfponding angle, in the original figure; wherefore, &c. We give the following, as a fpecimen of the fimplicity of an example given, to fupport and illuftrate the propofition. See fig. I. The plane g h i is parallel to the picture, A B; wherefore, the representation op is parallel to the original line, OP; ps is alfo Hh2 parallel parallel to PS; and, if os, OS be drawn, os will be parallel to OS, by Theo. Part ift. By Cor. 4. the angle o ps is equal to OPS; and by the second part of the theorem, op: OP:: ps: PS; for, each is as EC to E f. 66 Confequently, the triangles pos, POS are equi-angular; the angle o is equal O, and s equal S; and confequently, os: OS. : op: OP, or as ps: PS. "Therefore, the reprefentation, pos, is fimilar to the original triangle, POS. "For, SEOP may be fuppofed a pyramid, cut by a plane, A B, parallel to its bafe, POS. E, the eye, is the vertex of the pyramid." This theorem includes the knowledge, from which, the rules, applied in practice, are deduced, relative to objects whofe faces are fituated parallel to the picture. In the 13th theorem the general perfpective proportions of right lines, or portions of a right line, to each other, in respect of the originals, are, accurately and elegantly demonftrated. But, as thefe proportions are obtained (according to Brook Taylor, and others) by the true geometrical proportions, from the interfecting point, of the original line, only; and as that, in many cafes, would be difficult, if not impoffible to be obtained, we are here fhewn, that their diftances from the picture (which may be had) are in the fame ratio; and, as it does not depend on the real measures, either from the point of interfection, or from the picture, but their ratio to each other; that ratio is here fhewn to be determinable. As this is an effential point in the practice of perspective, and requires to be well understood, we shad give our readers the theorem. "The distance between the interfecting point of an original line, and the representation of any point in that line, is to the whole indefinite reprefentation: as the diftance between the original point and the interfecting point, is to the distance between the original point and the directing point of that line.” Now this perfpective ratio, of any original line, and the finite parts of that line, is well known to every mathematician, and practifed by every practitioner in perspective (on the true principles) though the ratio, here afcertained, perhaps, never en tered into his imagination. It is briefly and elegantly demonftrated. But, as this ratio of the feveral parts of the original line from its interfecting point (with the picture) is frequently unattainable, it is here, in a fubfequent corollary, proved, that their feveral diftances from the picture are in the fame ratio, as from the point in which the line would cut the picture. "For, whatever plane the original line is in, is not material, the diftance of the point, in queftion, from the picture, answers the fame purpose, as its diftance from the interfecting point of the line it is in; or, from the intersection of any plane with the picture in which that line is fituated. e, g. EX. NM is an original line cutting the picture, in the point I, in the interfection, A B, of the plane, NBC, that line is in; and the directing plane, DE C, in its directing point D. "I fay, that NF (the distance of the point N from the picture, AVB) is to FG, the diftance of the picture, as NI to ID (the distance of the point N from the interfecting point, to the diftance between the interfecting and directing points, of the line MN) or, as NA to AC, its distance from the interfection, to the distance be tween the interfection and directing line, of the plane the original line is in. "DEM. (For having joined IF and DG) because the directing plane is parallel to the picture, IF is parallel to DG. "Wherefore, the triangles GND, FNI are fimilar; and, for the fame reason, GNC, FNA, and alfo DNC, IN A are fimilar; confequently NF:NG:: NI: ND; or, as NA: NC. 4. 6 El. "Wherefore, the diftance of the original point from the picture, and the distance of the picture being known; the distance of its reprefentation, from the interfecting point, is a fourth proportional, viz. as the distance of the original point from the picture, added to the distance of the picture, i, e. as the distance NG (of the original point, N, from the directing plane) is to NF (the distance of that point from the picture) fo is the indefinite reprefentation, IV (of the original line MN) to In; the distance of n (the reprefentation of the point N) from I, the interfecting point of the original line. QE. D. It is, therefore, as NG: NF:: IV: In. For, (by the theorem) it is, inverfely, as ND: NI :: IV: In. Or, from the vanishing point, it will be, as NG: FG :: IV : nV. These two theorems, with the 9th and 12th, contain the whole theory of practical, rectilinear perspective. After which, in another fhort fection, is a brief theory of curvilinear perfpective; fo much as is neceffary to the art of delineating, in general. In the fixth and laft fection of this book, the author has undertaken to refute the feveral opinions, of fuch as have not a clear and juft idea of perfpective; who look on it as imperfect and fallacious, and confequently, not to be depended on, in many cafes, in practice. Our author, in this fection, fully and clearly explodes the abfurdity of fuch opinions; and manifeftly evinces, that they have no existence or foundation in the nature of things. The real fource of fuch erroneous opinions is pointed out, and how fuch mifreprefentations as gave rife to them, are to be avoided. That the chief, caufe of diftortion, in the picture, is owing to the abfurd pofition of it, in refpect of the object and the fpectator, and to its diftance. For he fhews, that notwithstanding the diftance of the eye from the object is sufficient to give the most Hh3 agrecable agreeable and natural representation; yet the picture being fitu ated, according to the common method of delineating fuch fituation renders that precaution utterly abortive; and, although it, perhaps, never once entered into the head of the delineator, that his picture muft neceffarily be viewed obliquely; yet, it is here made obvious, that it cannot poffibly reprefent the original, when feen direct. This fection, though apparently digreffive, from the main plan of the work, is perhaps one of the most valuable of the whole; as its tendency is to place the theory of perspective in a proper light, to diveft the reader of the prejudices he may have imbibed, from the old writers on the subject, and to prepare him for the next book, on the practice of perspective; whose rules (deduced from the foregoing theory, on principles the most certain and infallible) are univerfally applicable, and cannot, poffibly, by a perfon who knows their application, be productive of diftortion, or an unpleafing representation of the original object; except in fuch cafes as they have there been warned of, and fhewn how to avoid. But we must here take leave of this ingenious treatise for the prefent; referving our remarks on the remaining two books, together with what more is neceffary to the explanation of the other figures in the annexed plate, to another opportunity. To be concluded in our APPENDIX. ART. II. An Effay towards establishing the Melody and Measure of Speech to be expreffed and perpetuated by peculiar Symbols. 4to. 155. Almon. While we were lamenting the fcarcity of ingenious productions, and gravely reflecting on the ferious confequences of abiding by our plan, of giving the earliest account of all fuch, without making any referve for a dearth in the harveft of literature; we were agreeably furprifed with the appearance of the effay before us. On taking a curfory view however, of the preface, we were not a little pofed, at being told, toward the latter end of it, that without having a practical knowledge of modern mufic, it is next to impoffible, by theory alone, to comprehend it. For, moft unluckily for us, not forefeeing the utility, or, as our author intimates, the abfolute neceflity, of it, we made no provifion for the cafualty and have not one fiddler among us.-That we might do the author no injuftice, therefore, we called in, to our affist This circumftance puts us in mind of the famed author of Hurlothrombo, who being told by a man of rank and taste, that he could not understand his piece, replied, "On, Sir, that's because you did not read it with a fiddle under your am.”—A fidille Rick's-end fays my Lady, for fuch performances. ance ince, feveral of the best performers in our modern orchestras; from not one of which could we poffibly get the leaft information either theoretical or practical. They could all play very well on their favourite inftruments, nay could write mufic for any language, but, they frankly avowed, none of them could read words t. In this diftrefs we fat down, as mere literati, to review the prefent production; hoping, after all that, not being abfolutely amoufoi, we might give a tolerable account of the author's defign at leaft, though we profefs no dexterity in the management of a fiddle-stick. Not that we mean, by this ludicrous exordium, to depreciate the abilities of the author, or the merit of his work. On the contrary, we regard his elaborate inveftigation, of fo curious a fubject, as one of the most ingenious performances this age of invention and discovery (for fo it may be juftly called) has produced. That its utility is equal to its ingenuity, we pretend not to fay: and yet it is difficult to decide of the utility of purfuits, that tend to the improvement even of the polite arts and mere embellishments of human life. If we think, with the Mitylenians, that to be (ir aμabía nas àμsia) unlettered and unmufical, be the greatest misfortune in the world, the attempt, to unite the knowledge of letters with that of mufic, must be acknowledged, on all hands, deferving approbation and encouragement. The general defign of this author appears to be that of compar Unluckily we had not an 4 fon near us, though in juftice to another celebrated mufical compofer, we muft alfo make another diftinguishing exception; this faid compofer, who is (foi-difant) both a musician and poet, having declared to us, on a pretended perufal of this treatise, that the author's project is altogether chimerical. This declaration gives us not only reafon to believe the musical gentry in general will underftand it lefs, and do it lefs honour, than the learned, even though the latter thould happen to be amo:joi; but it reminds us alfo of the following epigrammatical fong, written fome years ago on a certain pretender to the restoration of the union between music and poetry. In vain of late did Dr. B. -- n, Harmonioutly the fiddlers play; You'd furely be delighted! Split, then, your goofe-quills, bards, or learn Go, and compofe fonatas. -; Or foon, I'll hold ye feven to fix, Will ferawl his own cantatas. * An oratorio fo called, wristen by the doctor. H h 4 ing |